JonathanB

No problem!

The area of a triangle is ( base * height ) / 2

So then A= (5*12)/2 = 30

Make the equation in terms of y = x

3x+qy = -q

3x = -q -  qy

3x = -q (1+y)

3x/ -q = 1+y

(-3x/q) - 1 = y 

slope equation y= mx +b

\((-3/q) *x -1 =y\)

mx = slope so then m = -3/q

Slope = -3q

Source:http://www.rocketmime.com/rockets/exp.html

exp means e^x where e is Euler's number

\(e(-4(1-(16.2/90.75)^2 = 0.0208055958562694​\)

Source:http://www.regentsprep.org/regents/math/algebra/ae7/expdecayl.htm

Exponential Growth Formula : 

\(y= a(1+r)^x\)

where a is the initial amount 

           r is the rate at which it increases 

           x is the time in which the growth occurs

Now plug it in:

a= 2.69 million

r= .04 (4%/100)

x=3

\(y=2.69(1+0.04)^x \)

\(y= 2.69(1+0.04)^3 = 3.02588416​\)

There will be about 3.03 million cars

1/cos(log(sqrt(sqrt(517)))) = 1.0000700949529581

1.0000700949529581^(351*28) = 1.9914620248323148696

1.9914620248323148696-1.9914620248314661 = 0.0000000000008487696

Sources: http://www.mathwarehouse.com/geometry/triangles/area/herons-formula-triangle-area.php

               https://www.mathsisfun.com/algebra/trig-cosine-law.html

Using the law of Cosines:

 \(C^2 = A^2 +B^2 - 2ABcos(c)\)

Where C is the unknown side

            A is one the known sides

            B is the other known side

            c is the angle between the two known sides

Now plug in values to find C

\(C^2 = 5^2 + 8^2 - 2(5)(8)cos105\) = \(109.7055 \)

\(\sqrt(C^2)= C\)

\(\sqrt(109.7055)\) = \(10.474 = 10.5 = C \)

Finding the area (using Heron's Formula);

\(Area= \sqrt(S(S-A)(S-B)(S-C)\)

where S is the semi-perimeter (half the perimeter)

           A is one of the sides

           B is another side

           C is the final side

Now to plug it in:

The area is 19.9

Give me a min

Source: https://sites.imsa.edu/acronym/2012/09/03/techniques-for-sleeping-in-class-2/

Drop a pencil on the floor. Put your hand as if your reaching for it. Put your head down and sleep. (While staying in that pose)

\(3 * 4^3- 6/ (2*3)\)

\(192-6/(6)\)

\(186/6\)

\(31\)